To estimate dimension of MNISTdigits the AE model uses 5 layer autoencoder. Table REF  defines the layers, activation function and regularizers. The input and output layer has 784 nodes; the output layer uses sigmoid [1]} activation function. To estimate dimension of financial market, using S&P 500 index constituents, we again use 5 layer autoencoder as illustrated in table REF . The input and output layer has 550S&P 500 index constituents change due to merger, acquisitions or new public listed companies being added to index. nodes and uses tanh[2]} activation function.
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